A graph, or static graph, \(G=(V,E)\)  is a set \(S\)  of vertices (or nodes) associated with a set \(E\)  of unordered pairs of vertices. In this paper, graphs will be without loop or multiple edges. The open neighbourhood of a vertex \(v\)  is \(N(v)=\lbrace u,(u,v) \in E\rbrace \) . For time varying graphs, we use the formalism and notations of a stream graph [1]}. We denote by \(S=(T,V,W,E)\)  a (stream) graph where \(T\)  is a set of instants, \(V\)  a finite set of nodes, \(W \subseteq T \times V\)  a set of temporal nodes and \(E= \subseteq T \times V \times V\)  a set of temporal links. We suppose that all the graphs are not looped nor directed. We denote by \(T_v=\lbrace t,(t,v)\in W\rbrace \)  and \(T_{uv}=\lbrace t,(t,u,v)\in E\rbrace \)  the sets of time instants at which \(v\)  and \((u,v)\)  are present respectively.
In a symmetrical way, we denote by \(V_t=\lbrace v,(t,v)\in W\rbrace \)  and \(E_t=\lbrace (u,v),(t,u,v)\in E\rbrace \)  the sets of vertices and edges present at time \(t\) . At the instantaneous level, \(G_t=(V_t,E_t)\)  is the graph induced by \(S\)  at time \(t\) . Of course, a link observed at time \(t\)  in \(G_t\)  may have begun before \(t\)  and may continue after \(t\) .
The instantaneous neighbourhood \(N_t\)  of a vertex \(v\)  is defined by \(N_t(v)=\lbrace (t,u),(t,(u,v)) \in E\rbrace \)  and is no more than the neighbourhood of \(v\)  in \(G_t\) . The instantaneous degree \(d_t(v)\)  of a vertex \(v\)  is the cardinal \(|N_t(v)|\)  of \(N_t(v)\) . In the following, we will essentially use instantaneous neighbourhoods, but we will also refer to the neighbourhood of a vertex in a time windows \(T^{\prime }\)  which is just \(N_{T^{\prime }}(v)=\bigcup _{T^{\prime }}N_t(v)\) . This is a disjoint union, and the cardinal of \(N_{T^{\prime }}(v)\)  is just the sum of the cardinals of the \(N_t(v)\) . In particular, \(N_T(v)\)  is the neighbourhood of \(v\)  over the whole period \(T\) .
